Eigenpairs of a Model Schrödinger Operator with Neumann Boundary Conditions

Virginie Bonnaillie-Noël (1) , Monique Dauge (1) , Nicolas Popoff (1) , Nicolas Raymond (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

The considered Schrödinger operator has a quadratic potential which is degenerate in the sense that it reaches its minimum all along a line which makes the angle \theta with the boundary of the half-plane where the problem is set. We exhibit localization properties for the eigenfunctions associated with its lowest eigenvalues below its essential spectrum. We investigate the densification and the asymptotics of the eigenvalues below the essential spectrum in the limit \theta\to 0.

Domaines: Analyse numérique [math.NA]

Virginie Bonnaillie-Noël, Monique Dauge, Nicolas Popoff, Nicolas Raymond. Eigenpairs of a Model Schrödinger Operator with Neumann Boundary Conditions. Waves 2011, Jul 2011, Vancouver, Canada. pp.715-717. ⟨hal-00616873⟩